Spectroscopy of a tunable moiré system with a correlated and topological flat band

Abstract

Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands. Here, we use gate-tuned scanning tunneling spectroscopy to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of electronic correlations and topology for its flat band. Our spectroscopic experiments are in agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands with a large effective g-factor.

Introduction

A moiré superlattice with flat electronic bands was first discovered by stacking two layers of graphene on top of each other at a precise angle^1,2,3. The flat band in magic angle twisted bilayer graphene (MATBG) emerges from the interplay between interlayer hybridization and monolayer graphene’ electronic structure and displays a plethora of correlated and topological phenomena. At partial band filling, MATBG shows a cascade of correlated insulating and superconducting phases, the underlying mechanisms of which are still being investigated^{3,4,5,6,7,3a. First, we highlight that changes of do** in TDBG caused by the V_SiG results in three clear jumps of the vHs marked by dashed white lines, indicating the Fermi energy is passing through a band gap. From these jumps, we identify the gate voltages corresponding to CNP (V_SiG = −3.5 V), full occupancy of the conduction band (72.5 V), and full occupancy of the valence band (−79.5 V). The appearance of CNP near zero gate voltage reveals that samples are not doped by impurities or by a significant work function difference between the sample and the STM tip. Furthermore, we find the gate voltage ranges required to occupy the conduction band and the valance band are identical: $\Delta {V}_{{\rm{SiG}}}$ = 76 V, which is also consistent with the carrier density needed to fill a moiré band of the 1.48° TDBG: n_S = 5.08*1012 cm−2 based on a parallel plate capacitance model (see Methods). These observations indicate that our sample is pristine, and our measurements are free from artifacts of tip-induced band bending, which was a concern in early STM studies of MATBG7,7). We observe clear jumps of spectral features when the Fermi energy crosses the full filling gaps. In the case that the tip does not have any gating effect, these jumps would occur at the same back gate voltage independent on bias voltage. However, tracing the full filling jumps, we notice a small change of fulling filling gate voltage depending on the bias voltage (Supplementary Fig. 7). From the slope of the discontinuity line, we can estimate the gating efficiency ratio between the tip and the back gate, which find 300 mV of the tip bias gating is comparable to 1 V of back gate voltage.}

Details on half-filling states

One may notice the half-filled states in Fig. 4 does not occur exactly at half filling. While we do not know the exact cause of this, it could be a result of nonlinear gating effect caused by mobile charged impurities inside the hBN or tip-induced band-bending effect⁸. We also cannot rule out the possibility of the correlated insulating state occurs slightly away from half filling in large twist angle TDBG devices. It is worth noting in previous transport studies, although the correlated insulator is commonly observed at half filling, sometimes it occur a little off from exact half filling²³.

Discussion on Supplementary Figs. 2 and 3

In Fig. 4a–c and Supplementary Figs. 2 and 3, we show several GT-STS measurements that provide information on the variation of such measurements at different areas of the same device as well as different locations within the moiré unit cell. Supplementary Fig. 2 shows a different type of data showing the signatures of correlations in the broadening and the visibility of the gap at the Fermi level in C1 can be different when measured on different locations or with different tip conditions. In Supplementary Fig. 3, we include more GT-STS measurements presented together with STM topographs that show areas 1–4. The location of the corresponding measurements within the unit cell are marked on these topographs (Supplementary Fig. 3a–d). Spectrums in Supplementary Fig. 2 (Supplementary Fig. 3h), which shows two peaks of C1 band, with one peak crossing the Fermi level and further split around the half filling, appear to the very different from other data set (Supplementary Fig. 3a–c). The difference could be caused by the different locations where the data is taken, but it could also be caused by anomalous tip condition in acquiring Supplementary Fig. 2.